On multipole approximations of the Fokker-Planck-Landau operator
In this paper we are concerned with numerical approximations of the Fokker-Planck-Landau operator which is used to describe collisions between charged particles in a plasma. Our aim is to construct accurate approximations to this operator that have a reduced numerical complexity and still satisfy some important physical properties of conservation and entropy. After a brief description of some recent works on the discretizations of such an operator, we focus on the application of the well-known Fast Multipole Method (FMM) to the approximation of the three dimensional Fokker-Planck-Landau operators and review the results in . In the same spirit but in the simpler case of a spherical geometry, we give a short presentation of an alternative method that uses wavelet approximation techniques. Then, we check the efficiency of the multipole method in terms of accuracy and computational cost and present some numerical tests at the end of the paper.
KeywordsCollision Operator Entropy Inequality Multipole Expansion Fast Multipole Method Wavelet Approximation
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